On the Spectrum of Neutron Transport Equations with Reflecting Boundary Conditions

This dissertation is devoted to investigating the time dependent neutron transport equations with reflecting boundary conditions. Two typical geometries --- slab geometry and spherical geometry --- are considered in the setting of <I>L^p</I> including <I>L^1</I>. Some aspects of the spectral properties of the transport operator <I>A</I> and the strongly continuous semigroup <I>T(t)</I> generated by <I>A</I> are studied. It is shown under fairly general assumptions that the accumulation points of { m Pas}(A):=sigma (A) cap { lambda :{ m Re}lambda > -lambda^{ast} }, if they exist, could only appear on the line { m Re}lambda =-lambda^{ast}, where lambda^{ast} is the essential infimum of the total collision frequency. The spectrum of <I>T(t)</I> outside the disk {lambda : |lambda| leq exp (-lambda^{ast} t)} consists of isolated eigenvalues of <I>T(t)</I> with finite algebraic multiplicity, and the accumulation points of sigma (T(t)) igcap{ lambda : |lambda| > exp (-lambda^{ast} t)}, if they exist, could only appear on the circle {lambda :|lambda| =exp (-lambda^{ast} t)}. Consequently, the asymptotic behavior of the time dependent solution is obtained.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2000

Author dc:creator

• Song, Degong

Chair dc:contributor.committeechair

• Greenberg, William

Committee members dc:contributor.committeemember

• Haskell, Peter E.
• Kohler, Werner E.
• Klaus, Martin
• Hagedorn, George A.

• transport equation
• spectrum
• stability
• strongly continuous semigroup

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-03072000-23200015

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/26375